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Volume of Polyhedra

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Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.

A pre-requisite to figuring out the volume of a cube cut by a plane is to calculate the volume of a polyhedron, be it convex or non-convex.

The tool and data in polyhedra_volume.tbz compute the volume for 10 tetrahedra, 5 cubes, 5 regular octahedra, 5 rhombic dodecaheda, 1 regular dodecahedron, 1 regular icosahedron, 1 rhombic triacontahedron, 1 disdyakis triacontahedron (left image below), 1 snub cube, and 1 small stellated dodecahedron (non-convex, right image below). Guidance is given in the tool on how to create data files for other polyhedra. The calculated volumes of these polyhedra are then compared to the volumes given by Mathematica, with the differences shown to be near floating point zero.






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Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer co-authorship as appropriate.